In a two-part equilibrium study, in the second experiment adding heat increases the concentration at equilibrium; what does this imply about the reaction enthalpy and the temperature dependence of the equilibrium constant?

If adding heat increases the equilibrium concentration of the species being monitored in the second experiment, the shift is toward the endothermic direction for that species, implying \(\Delta H^\circ>0\) for the forward formation of that species and an increase of \(K\) with temperature.

In the second experiment adding heat increases the concentration

Accepted answer Answer included

Meaning of “in the second experiment adding heat increases the concentration”

The observation “in the second experiment adding heat increases the concentration” has a standard equilibrium interpretation: the equilibrium composition after heating contains more of the monitored species than before heating. In chemical equilibrium, that composition change reflects a temperature-driven shift of the equilibrium position and a temperature-driven change of the equilibrium constant.

Thermochemical interpretation of heat addition

Heat behaves like a reactant for an endothermic direction and like a product for an exothermic direction. A compact representation uses “heat” on the appropriate side of the equilibrium:

\[ \text{endothermic forward:}\quad \text{Reactants} + \text{heat} \rightleftharpoons \text{Products} \]

\[ \text{exothermic forward:}\quad \text{Reactants} \rightleftharpoons \text{Products} + \text{heat} \]

Key conclusion from the concentration increase

An increase in the equilibrium concentration of the monitored species upon heating indicates that the equilibrium shift favors the direction that absorbs heat for producing that species. In the common convention where the monitored species is a product of the written forward reaction, the implication is \(\Delta H^\circ > 0\) for the forward reaction.

Equilibrium constant as a function of temperature

The equilibrium constant depends on temperature and does not depend on initial concentrations directly. For a general reaction \(aA + bB \rightleftharpoons cC + dD\), the concentration form is

\[ K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}. \]

Heating changes the value of \(K_c\) when \(\Delta H^\circ \neq 0\). The van’t Hoff relationship expresses this dependence:

\[ \frac{d(\ln K)}{dT}=\frac{\Delta H^\circ}{R T^{2}}. \]

The sign of \(\Delta H^\circ\) controls the direction of change of \(K\) with temperature: \(\Delta H^\circ > 0\) implies \(K\) increases as \(T\) increases, and \(\Delta H^\circ < 0\) implies \(K\) decreases as \(T\) increases.

Interpretation framed as a two-experiment comparison

A frequent laboratory design uses two experiments with the same chemical system but different thermal disturbances. The second experiment result, “in the second experiment adding heat increases the concentration,” aligns with an endothermic shift toward the monitored species. A representative example is the gas-phase equilibrium

\[ \mathrm{N_2O_4(g)} \rightleftharpoons 2\,\mathrm{NO_2(g)} \qquad (\Delta H^\circ > 0 \text{ for the forward direction}), \]

where heating increases the equilibrium amount and concentration of \(\mathrm{NO_2}\) (often detected by a stronger brown color), consistent with \(K\) increasing with temperature for an endothermic forward reaction.

Assumptions that make “concentration increases” chemically meaningful

A concentration change attributed to equilibrium shift presumes a comparison between equilibrium states at two temperatures under controlled conditions. The following conditions support that interpretation in general chemistry contexts.

Closed system: no loss or gain of matter during heating
Equilibrium established at each temperature before measurement
Rigid container or clearly defined solution volume during comparison
Monitored species concentration reported as an equilibrium composition measure (not an instantaneous thermal expansion artifact)

The second experiment shows an increase in equilibrium concentration after heating, consistent with a shift toward the endothermic direction for forming the monitored species and a corresponding increase of \(K\) with temperature when \(\Delta H^\circ > 0\).

Common pitfalls

Rate versus equilibrium: faster approach to equilibrium versus a changed equilibrium position
Concentration definition in gases: composition shift versus pressure increase from heating at fixed volume
Sign convention for \(\Delta H^\circ\): endothermic direction aligned with the side that consumes heat
Equilibrium constant dependence: \(K\) temperature dependence present even when concentration units appear unchanged

Vote on the accepted answer

Upvotes: 0 Downvotes: 0 Score: 0